Evidence of Change in the Density of States during the Martensitic Phase Transformation of Ni-Mn-In Metamagnetic Shape Memory Alloys

Specific heat measurements were performed at low temperatures for Ni50Mn50−xInx alloys to determine their Debye temperatures (θD) and electronic specific heat coefficients (γ). For x ≤ 15, where the ground state is the martensite (M) phase, θD decreases linearly and γ increases slightly with increasing In content. For x ≥ 16.2, where the ground state is the ferromagnetic parent (P) phase, γ increases with decreasing In content. Extrapolations of the composition dependences of θD and γ in both the phases suggest that these values change discontinuously during the martensitic phase transformation. The value of θD in the M phase is larger than that in the P phase. The behavior is in accordance with the fact that the volume of the M phase is more compressive than that of the P phase. On the other hand, γ is slightly larger in the P phase, in good agreement with the reported density of states around the Fermi energy obtained by the first-principle calculations.


Introduction
Since a unique martensitic phase transformation in off-stoichiometric Heusler NiMnZ (Z = In, Sn, and Sb) alloys were first reported by Sutou et al. [1], NiMnIn-and NiMnSn-based alloys have attracted widespread interest as high-performance multiferroic materials.The alloys show many interesting properties, such as metamagnetic shape memory effect [2,3] inverse magnetocaloric effect [4][5][6], giant magnetoresistance effect [7,8], and giant magnetothermal conductivity [9].These interesting physical properties are related to drastic changes in magnetic properties between the ferromagnetic parent (P) phase and the martensite (M) phase with weak magnetism.Such large changes of the various physical properties should be due to the change in the electronic state during the martensitic phase transformation.First-principles density-functional calculations and hard X-ray photoelectron spectroscopy (HAXPES) experiments were performed to investigate the electronic states in the P and M phases of Ni-Mn-In alloys [10].In these calculations, composition dependence of the partial density of states (DOS) in the P phase for Ni-Mn-In was investigated using the periodic supercells, in addition to that in the M phase, where tetragonal distortion was introduced.The valence-band photoelectron spectra of the Ni 50 Mn 34 In 16 alloy in warming and cooling processes showed that the peak near the Fermi energy (E F ) in the P phase disappeared in the M phase temperature range, suggesting the formation of the pseudo-gap.The minority-spin Ni 3d-e g state has also been concluded to play an important role in stabilizing the M phase in off-stoichiometric composition [10].
Herein, we performed specific heat measurements in Ni-Mn-In alloy system to investigate the electronic specific heat coefficient (γ), which will provide information on the DOS around E F , and the Debye temperature (θ D ).The obtained results may provide indirect information on the electronic state, in contrast to the photoelectron spectroscopy observations that provide direct information.However, it has been reported that the value of γ for L1 0 -type NiMn alloy and related materials (i.e., PdMn and PtMn) where the existence of the pseudo-gap around E F characterizes their unique electronic states agrees well with the value obtained by theoretical calculations [11][12][13].Systematic study of the specific heat measurements in a wide composition region for Ni-Mn-In will help understand the behavior of the metamagnetic shape memory alloys in this system.

Experimental Procedure
Ni 50 Mn 50−x In x (0 ≤ x ≤ 25) alloys were fabricated by induction melting in an Ar atmosphere.The specimens were sealed in a quartz capsule and were annealed at 1173 K for 1 day before quenching in water.The microstructure and composition were confirmed by the electron probe microanalyzer.The crystal structure was investigated by powder X-ray diffraction and transmission electron microscope observations.The related results were reported in the previous paper [14].The magnetic measurements were carried out on a superconducting quantum interference device (SQUID; Quantum Design Ltd., San Diego, CA, USA) magnetometer.Specific heat measurements were carried out by the relaxation method using a physical properties measurement system (PPMS produced by Quantum Design Ltd., San Diego, CA, USA) at temperatures below 20 K.The absolute value of the specific heat was checked by measuring one of the standard pure Cr.

Magnetic Measurements
Figure 1a,b show magnetization (M-H) curves obtained at 5 K and thermomagnetization (M-T) curves obtained under a magnetic field of 10 kOe for Ni 50 Mn 50−x In x alloy specimens having x ≤ 15, respectively.Here, the ground state of the specimens is the martensite (M) phase.The specimen with x = 0 (NiMn) has been reported to be collinear-type antiferromagnetic with the Néel temperature higher than the martensitic transformation temperature [15].Therefore, the magnetic state is deduced to be antiferromagnetic for low In concentrations, and the antiferromagnetic exchange interaction in the system decreases with increasing In content [16,17].The NiMn has an L1 0 -type tetragonal structure with lattice parameters of a = 0.374 and c = 0.352 nm, and it transforms to B2-type cubic one at the martensitic transformation temperature [15].With increasing the In concentration, the crystal structure of M phase varies to 14 M and 10 M stacking monoclinic structures [14,18,19].The straight line in the M-H curves (Figure 1a) is characteristic of the antiferromagnetic properties.The slope increases with increasing In content, and the M-H curve indicates small hysteresis at x = 13.In the M-H curve for x = 15 (inset of Figure 1a), large hysteresis is observed, and magnetization tends to saturation.This variation arises in the magnetization curves because ferromagnetic exchange interaction is introduced with increasing In content.AC magnetization measurements have suggested that the ground state for x = 15 is the blocking state, showing frequency dependence in both the real and imaginary parts of the susceptibility [20].The variation of magnetic property from the antiferromagnetic state to the blocking state is also confirmed by the M-T curves for Ni 50 Mn 50−x In x alloys with x ≤ 15.In the measurements for obtaining the M-T curves, the specimens were cooled to low temperatures in zero magnetic field, and the magnetization was measured in warming process and cooling process under the same applied magnetic field.Magnetization at lower temperatures gradually increases with increasing In content, and magnetic field cooling effect is observed for x = 10, 13, and 15.The large magnetization change observed at ~300 K in the M-T curve for x = 15 (inset of Figure 1b) is due to the martensitic phase transformation, and the magnetic property at temperatures just below the transition temperature has been concluded to be paramagnetic based on Mössbauer spectroscopy [21].
These results along with previous reports on AC magnetization measurements [20], suggest that antiferromagnetic long-range ordering might have disappeared somewhere in the composition region.
M-H curves obtained at 5 K and M-T curves obtained under a magnetic field of 500 Oe for specimens with x ≥ 16.2 in Ni 50 Mn 50−x In x alloys are shown in Figure 2a,b, respectively.Here, the ground state of the system is the ferromagnetic parent (P) phase.That is, no martensitic transformation occurs down to low temperatures in these composition regions.The crystal structure is basically the L2 1 -type structure.The lattice parameter has been reported to a = 0.6071 nm for the x = 25 at room temperature and to decrease linearly with increasing the Mn composition [22].The Figure 2b shows only warming process in M-T curves because there is almost no magnetic field cooling effect, in contrast to that for x ≤ 15 in Figure 1b.The saturated magnetization increases with decreasing In content from the stoichiometric composition of Ni 50 Mn 25 In 25 (=Ni 2 MnIn).On the other hand, concentration dependence of the Curie temperature (T C ) does not show the systematic variation as is shown by saturation magnetization.Figure 2b shows that the value of T C is ~320 K, independent of In content.
Metals 2017, 7, 414 3 of 8 measurements [20], suggest that antiferromagnetic long-range ordering might have disappeared somewhere in the composition region.M-H curves obtained at 5 K and M-T curves obtained under a magnetic field of 500 Oe for specimens with x ≥ 16.2 in Ni50Mn50−xInx alloys are shown in Figure 2a,b, respectively.Here, the ground state of the system is the ferromagnetic parent (P) phase.That is, no martensitic transformation occurs down to low temperatures in these composition regions.The crystal structure is basically the L21-type structure.The lattice parameter has been reported to a = 0.6071 nm for the x = 25 at room temperature and to decrease linearly with increasing the Mn composition [22].The Figure 2b shows only warming process in M-T curves because there is almost no magnetic field cooling effect, in contrast to that for x ≤ 15 in Figure 1b.The saturated magnetization increases with decreasing In content from the stoichiometric composition of Ni50Mn25In25 (= Ni2MnIn).On the other hand, concentration dependence of the Curie temperature (TC) does not show the systematic variation as is shown by saturation magnetization.Figure 2b shows that the value of TC is ~320 K, independent of In content.measurements [20], suggest that antiferromagnetic long-range ordering might have disappeared somewhere in the composition region.
M-H curves obtained at 5 K and M-T curves obtained under a magnetic field of 500 Oe for specimens with x ≥ 16.2 in Ni50Mn50−xInx alloys are shown in Figure 2a,b, respectively.Here, the ground state of the system is the ferromagnetic parent (P) phase.That is, no martensitic transformation occurs down to low temperatures in these composition regions.The crystal structure is basically the L21-type structure.The lattice parameter has been reported to a = 0.6071 nm for the x = 25 at room temperature and to decrease linearly with increasing the Mn composition [22].The Figure 2b shows only warming process in M-T curves because there is almost no magnetic field cooling effect, in contrast to that for x ≤ 15 in Figure 1b.The saturated magnetization increases with decreasing In content from the stoichiometric composition of Ni50Mn25In25 (= Ni2MnIn).On the other hand, concentration dependence of the Curie temperature (TC) does not show the systematic variation as is shown by saturation magnetization.Figure 2b shows that the value of TC is ~320 K, independent of In content.[22] and the theoretically calculated one for the stoichiometric composition [23].Here, I s is determined by linear extrapolation of the M 2 versus H/M curve to H/M = 0 (Arrott plot), from the data in Figure 2a.I s increases almost linearly with decreasing In content, or in other words, with increasing Mn content.For the stoichiometric composition of Ni 50 Mn 25 In 25 (=Ni 2 MnIn), the Ni atoms locate at the 8c site, and the Mn and In atoms at the 4a and 4b sites in the Wyckoff position, respectively.In the present series of the specimens, excess Mn substituted for In at the 4b site.Therefore, the increasing of I s with increasing the Mn means that the magnetic moment of Mn atoms at the 4b site couples ferromagnetically with that of the Mn atoms at the ordinary site (4a site).A solid straight line is drawn, assuming that the magnitude of the magnetic moment of Mn at the 4b site is the same as that of Mn at the 4a site, and the experimental values are in good agreement with the expected line [24].Here, the values of the magnetic moments (m) are used as m Mn = 3.719, m Ni = 0.277 and m In = −0.066µ B , which are obtained the first principle calculation [23].The T C values for all the specimens with x ≥ 16.2 are similar (the variation is <15 K) and they are independent to the composition.This behavior suggests that the T C is governed by the exchange interaction between Mn atoms at the 4a site, and the interaction by the Mn atoms at the 4b site does not affect the total exchange interaction in the system.This behavior of T C was studied earlier over a wide concentration region by Miyamoto et al. [25], who reported that T C decreases drastically with increases In concentration in Ni 50 Mn 50−y In y alloys with y > 25.Here, excess In substituted the Mn atoms at the 4a site, therefore, the decrease in T C is probably caused by the lack of Mn-Mn exchange interactions at the 4a site, if the magnetic moment of Mn atoms are assumed not to change.[22] and the theoretically calculated one for the stoichiometric composition [23].Here, Is is determined by linear extrapolation of the M 2 versus H/M curve to H/M = 0 (Arrott plot), from the data in Figure 2a.Is increases almost linearly with decreasing In content, or in other words, with increasing Mn content.For the stoichiometric composition of Ni50Mn25In25 (= Ni2MnIn), the Ni atoms locate at the 8c site, and the Mn and In atoms at the 4a and 4b sites in the Wyckoff position, respectively.In the present series of the specimens, excess Mn substituted for In at the 4b site.Therefore, the increasing of Is with increasing the Mn means that the magnetic moment of Mn atoms at the 4b site couples ferromagnetically with that of the Mn atoms at the ordinary site (4a site).A solid straight line is drawn, assuming that the magnitude of the magnetic moment of Mn at the 4b site is the same as that of Mn at the 4a site, and the experimental values are in good agreement with the expected line [24].Here, the values of the magnetic moments (m) are used as mMn = 3.719, mNi = 0.277 and mIn = -0.066μB, which are obtained from the first principle calculation [23].The TC values for all the specimens with x ≥ 16.2 are similar (the variation is <15 K) and they are independent to the composition.This behavior suggests that the TC is governed by the exchange interaction between Mn atoms at the 4a site, and the interaction by the Mn atoms at the 4b site does not affect the total exchange interaction in the system.This behavior of TC was studied earlier over a wide concentration region by Miyamoto et al. [25], who reported that TC decreases drastically with increases In concentration in Ni50Mn50−yIny alloys with y > 25.Here, excess In substituted the Mn atoms at the 4a site, therefore, the decrease in TC is probably caused by the lack of Mn-Mn exchange interactions at the 4a site, if the magnetic moment of Mn atoms are assumed not to change.2a, along with reported experimental and theoretically calculated values [22,23], and of the Curie temperature (TC) for Ni50Mn50−xInx alloys with x ≥ 16.2.The solid straight line for Is is simulated assuming that the excess Mn atoms have same magnetic moment as that of Mn at the ordinary sites and couples ferromagnetically [24].The solid line for TC is guide to the eye.

Specific Heat Measurements
Figure 4a,b show the relationship between specific heat (C) and temperature (T) in C/T-T 2 plots for x ≤ 15 and x ≥ 16.2, respectively, the insets show C-T plots for each specimen.The specific heat is generally expressed as the summation of some contributions like electronic, lattice, and magnetic contributions.When the experiments are performed at low temperatures, the magnetic excitation has little contribution to the specific heat and the other two components become dominant as follows [26]: where, the first and second terms are the electronic and lattice contributions, respectively, in which γ is the electronic specific heat coefficient and β is the lattice coefficient.In the classical model, γ is  2a, along with reported experimental and theoretically calculated values [22,23], and of the Curie temperature (T C ) for Ni 50 Mn 50−x In x alloys with x ≥ 16.2.The solid straight line for I s is simulated assuming that the excess Mn atoms have same magnetic moment as that of Mn at the ordinary sites and couples ferromagnetically [24].The solid line for T C is guide to the eye.

Specific Heat Measurements
Figure 4a,b show the relationship between specific heat (C) and temperature (T) in C/T-T 2 plots for x ≤ 15 and x ≥ 16.2, respectively, the insets show C-T plots for each specimen.The specific heat is generally expressed as the summation of some contributions like electronic, lattice, and magnetic contributions.When the experiments are performed at low temperatures, the magnetic excitation has little contribution to the specific heat and the other two components become dominant as follows [26]: where, the first and second terms are the electronic and lattice contributions, respectively, in which γ is the electronic specific heat coefficient and β is the lattice coefficient.In the classical model, γ is thought to correspond to the total DOS.In the C/T-T 2 plot, when a linear relationship is obtained, γ and β are given by the intercept and the slope, respectively.Furthermore, θ D is given by the relation where R is the gas constant [26].As shown in Figure 4a,b, a linear relationship is obtained, and the behaviors of these coefficients in terms of composition are different in each figure (i.e., in the M phase and in the P phase).In Figure 4a, for specimens with x ≤ 15, in which the ground state is the M phase, γ increases with increasing In content.The slope also increases, corresponding to the decrease of θ D .On the other hand, in Figure 4b for specimens with x ≥ 16.2, in which the ground state is the ferromagnetic P phase, γ changes slightly and slope is increased with increasing In content.
Metals 2017, 7, 414 5 of 8 thought to correspond to the total DOS.In the C/T-T 2 plot, when a linear relationship is obtained, γ and β are given by the intercept and the slope, respectively.Furthermore, θD is given by the relation where R is the gas constant [26].As shown in Figure 4a,b, a linear relationship is obtained, and the behaviors of these coefficients in terms of composition are different in each figure (i.e., in the M phase and in the P phase).In Figure 4a, for specimens with x ≤ 15, in which the ground state is the M phase, γ increases with increasing In content.The slope also increases, corresponding to the decrease of θD.
On the other hand, in Figure 4b for specimens with x ≥ 16.2, in which the ground state is the ferromagnetic P phase, γ changes slightly and slope is increased with increasing In content.Concentration dependences of γ and θD in Ni50Mn50−xInx alloys are shown in Figure 5, together with the reported values of γ = 0.31 mJ/mol-K 2 and θD = 422 K for x = 0 [11].The θD value decreases linearly with increasing In content in the M phase region.It has been reported that the crystal structure changes continuously from L10-type tetragonal structure for x = 0 to monoclinic multilayered stacking structure with increasing In content [18].Magnetic property is collinear-type antiferromagnetic with high Néel temperature for x = 0 [15].This property changes to complicated magnetic properties, in which long-range magnetic ordering is absent and blocking behavior is observed [18,21].Since neither crystal structure nor magnetic properties change sharply with changing In content, the decrease in θD may be caused by the substitution effect of the heavy element In.In the M phase range, γ increases gradually with increasing In content.The electronic state of x = 0 is characterized by the formation of a clear pseud-gap around EF and it has been reported that the total DOS is significantly low and the unique electronic state may correlate with the high antiferromagnetic stability [11].Gradual increase of γ in M phase region would be due to the loss in antiferromagnetic stability.
In the P phase region, both γ and θD increase with decreasing In content.Although the variation of θD is similar to that observed in the M phase, the values do not coincide in the middle composition region.From the extrapolations in both the phases (the dotted lines for θD), it seems that θD changes discontinuously around x = 15, the difference corresponds to the change in θD during the martensitic phase transformation.Overall, θD in the M phase is larger than that in the P phase, in accordance with the experimental fact that the volume of the M phase is more compressive than that of the P phase [27].The variation of γ agrees well with the value obtained by first-principle density-functional calculations [10].DOS in the P phase for the stoichiometric and off-stoichiometric compositions have been calculated, and γ values converted from total DOS are also plotted in Figure 5. DOS in the M phase was also calculated by applying the lattice distortion.The gradual increase of γ in the P phase Concentration dependences of γ and θ D in Ni 50 Mn 50−x In x alloys are shown in Figure 5, together with the reported values of γ = 0.31 mJ/mol•K 2 and θ D = 422 K for x = 0 [11].The θ D value decreases linearly with increasing In content in the M phase region.It has been reported that the crystal structure changes continuously from L1 0 -type tetragonal structure for x = 0 to monoclinic multi-layered stacking structure with increasing In content [18].Magnetic property is collinear-type antiferromagnetic with high Néel temperature for x = 0 [15].This property changes to complicated magnetic properties, in which long-range magnetic ordering is absent and blocking behavior is observed [18,21].Since neither crystal structure nor magnetic properties change sharply with changing In content, the decrease in θ D may be caused by the substitution effect of the heavy element In.In the M phase range, γ increases gradually with increasing In content.The electronic state of x = 0 is characterized by the formation of a clear pseud-gap around E F and it has been reported that the total DOS is significantly low and the unique electronic state may correlate with the high antiferromagnetic stability [11].Gradual increase of γ in M phase region would be due to the loss in antiferromagnetic stability.
In the P phase region, both γ and θ D increase with decreasing In content.Although the variation of θ D is similar to that observed in the M phase, the values do not coincide in the middle composition region.From the extrapolations in both the phases (the dotted lines for θ D ), it seems that θ D changes discontinuously around x = 15, the difference corresponds to the change in θ D during the martensitic phase transformation.Overall, θ D in the M phase is larger than that in the P phase, in accordance with the experimental fact that the volume of the M phase is more compressive than that of the P phase [27].The variation of γ agrees well with the value obtained by first-principle density-functional calculations [10].DOS in the P phase for the stoichiometric and off-stoichiometric compositions have been calculated, and γ values converted from total DOS are also plotted in Figure 5. DOS in the M phase was also calculated by applying the lattice distortion.The gradual increase of γ in the P phase is in accordance with that obtained by calculations.The theoretical calculations have shown that the minor peak corresponding to the Ni-3d e g state appears at the energy level of −0.1 eV from E F in the minority band for the off-stoichiometric composition, and the minority peak shifts closer to the E F with increasing In content.Therefore, the shift in the minor peak will increase the total DOS because the DOS in the majority band is independent of the In content.Furthermore, the experimental value of γ at x = 13 is almost the same as the calculated one.Based on the extrapolations of the concentration dependence of γ in both the phases, a change in DOS is expected in the transformation.In other words, DOS is reduced when the P phase transforms to the M phase.This behavior has also been explained by the theoretical calculations that the minority-spin Ni-3d x 2 -y 2 splits on introducing the lattice distortion and a pseudo-gap is formed at E F [10].The other calculation also suggested that the splitting of the Ni-3d e g states around E plays an important role in occurrence of the martensitic transformation in the off-stoichiometric Ni-Mn-In alloy [28].
Metals 2017, 7, 414 6 of 8 is in accordance with that obtained by calculations.The theoretical calculations have shown that the minor peak corresponding to the Ni-3d eg state appears at the energy level of −0.1 eV from EF in the minority band for the off-stoichiometric composition, and the minority peak shifts closer to the EF with increasing In content.Therefore, the shift in the minor peak will increase the total DOS because the DOS in the majority band is independent of the In content.Furthermore, the experimental value of γ at x = 13 is almost the same as the calculated one.Based on the extrapolations of the concentration dependence of γ in both the phases, a change in DOS is expected in the transformation.In other words, DOS is reduced when the P phase transforms to the M phase.This behavior has also been explained by the theoretical calculations that the minority-spin Ni-3d x 2 -y 2 splits on introducing the lattice distortion and a pseudo-gap is formed at EF [10].The other calculation also suggested that the splitting of the Ni-3d eg states around EF plays an important role in occurrence of the martensitic transformation in the off-stoichiometric Ni-Mn-In alloy [28].[10] and reported ones for x = 0 [11].The blue and light blue circles are θD in M phase and P phase, respectively, and the red and pink circles are γ in M phase and P phase, respectively.The four lines are guide to the eye.

Conclusions
Specific heat measurements were performed at low-temperatures in Ni50Mn50−xInx alloys for 0 ≤ x ≤ 25 to investigate the concentration dependences of electronic specific heat coefficient (γ) and the Debye temperature (θD) over a wide concentration region.In the martensite (M) phase (x ≤ 15), θD decreases linearly and γ increases with increasing In content.The change in θD attributed to the substitution effect by the heavy element In.The increase in γ is attributed to the change in the density of states (DOS), and the clear pseudo-gap formed around the Fermi energy (EF) may widen with the disappearance of the strong antiferromagnetism in L10-type NiMn equiatomic alloy, whereas the pseudo-gap is somewhat maintained within the M phase.
In the ferromagnetic parent (P) phase (x ≥ 16.2), γ increases with decreasing In content.The change in DOS, in accordance with the first-principle density-functional calculation results reported earlier, is that the minor peak in the minority band shifts closer to EF with decreasing In content.From the extrapolations of the composition dependences of γ and θD from both the phase regions, these values should change discontinuously during the martensitic phase transformation.The value of θD in the M phase is larger than that in the P phase, in accordance with the fact that the volume of the M phase is more compressive than that of the P phase.It is suggested that the DOS in P phase decreases during martensitic phase transformation.This behavior is explained by the theoretical calculations that the Ni-3d eg band splits in the M phase and the pseudo-gap is formed around the EF.[10] and reported ones for x = 0 [11].The blue and light blue circles are θ D in M phase and P phase, respectively, and the red and pink circles are γ in M phase and P phase, respectively.The four lines are guide to the eye.

Conclusions
Specific heat measurements were performed at low-temperatures in Ni 50 Mn 50−x In x alloys for 0 ≤ x ≤ 25 to investigate the concentration dependences of electronic specific heat coefficient (γ) and the Debye temperature (θ D ) over a wide concentration region.In the martensite (M) phase (x ≤ 15), θ D decreases linearly and γ increases with increasing In content.The change in θ D attributed to the substitution effect by the heavy element In.The increase in γ is attributed to the change in the density of states (DOS), and the clear pseudo-gap formed around the Fermi energy (E F ) may widen with the disappearance of the strong antiferromagnetism in L1 0 -type NiMn equiatomic alloy, whereas the pseudo-gap is somewhat maintained within the M phase.
In the ferromagnetic parent (P) phase (x ≥ 16.2), γ increases with decreasing In content.The change in DOS, in accordance with the first-principle density-functional calculation results reported earlier, is that the minor peak in the minority band shifts closer to E F with decreasing In content.From the extrapolations of the composition dependences of γ and θ D from both the phase regions, these values should change discontinuously during the martensitic phase transformation.The value of θ D in the M phase is larger than that in the P phase, in accordance with the fact that the volume of the M phase is more compressive than that of the P phase.It is suggested that the DOS in P phase decreases during martensitic phase transformation.This behavior is explained by the theoretical calculations that the Ni-3d e g band splits in the M phase and the pseudo-gap is formed around the E F .

Figure 1 .
Figure 1.(a) Magnetization curves at 5 K and (b) thermomagnetization curves measured at 10 kOe for the specimens with x ≤ 15 in Ni50Mn50−xInx alloys.The arrows in the figures mean applying and removing magnetic fields in (a), and the warming and cooling processes in (b).Here, the ground state of the specimens is the martensite phase.The insets are those for x = 15.

Figure 2 .
Figure 2. (a) Magnetization curves at 5 K and (b) thermomagnetization curves measured at 500 Oe in the warming process for the specimens with x ≥ 16.2 in Ni50Mn50−xInx alloys.Here, the ground state of the system is the ferromagnetic parent phase and no martensitic transformation occurs down to low temperatures.

Figure 1 .
Figure 1.(a) Magnetization curves at 5 K and (b) thermomagnetization curves measured at 10 kOe for the specimens with x ≤ 15 in Ni 50 Mn 50−x In x alloys.The arrows in the figures mean applying and removing magnetic fields in (a), and the warming and cooling processes in (b).Here, the ground state of the specimens is the martensite phase.The insets are those for x = 15.

Figure 1 .
Figure 1.(a) Magnetization curves at 5 K and (b) thermomagnetization curves measured at 10 kOe for the specimens with x ≤ 15 in Ni50Mn50−xInx alloys.The arrows in the figures mean applying and removing magnetic fields in (a), and the warming and cooling processes in (b).Here, the ground state of the specimens is the martensite phase.The insets are those for x = 15.

Figure 2 .
Figure 2. (a) Magnetization curves at 5 K and (b) thermomagnetization curves measured at 500 Oe in the warming process for the specimens with x ≥ 16.2 in Ni50Mn50−xInx alloys.Here, the ground state of the system is the ferromagnetic parent phase and no martensitic transformation occurs down to low temperatures.

Figure 2 .
Figure 2. (a) Magnetization curves at 5 K and (b) thermomagnetization curves measured at 500 Oe in the warming process for the specimens with x ≥ 16.2 in Ni 50 Mn 50−x In x alloys.Here, the ground state of the system is the ferromagnetic parent phase and no martensitic transformation occurs down to low temperatures.

Figure 3
Figure3indicates concentration dependences of saturation magnetization (I s ) and T C for Ni 50 Mn 50−x In x alloys with x ≥ 16.2, together with reported experimental values[22] and the theoretically calculated one for the stoichiometric composition[23].Here, I s is determined by linear extrapolation of the M 2 versus H/M curve to H/M = 0 (Arrott plot), from the data in Figure2a.I s increases almost linearly with decreasing In content, or in other words, with increasing Mn content.For the stoichiometric composition of Ni 50 Mn 25 In 25 (=Ni 2 MnIn), the Ni atoms locate at the 8c site, and the Mn and In atoms at the 4a and 4b sites in the Wyckoff position, respectively.In the present series of the specimens, excess Mn substituted for In at the 4b site.Therefore, the increasing of I s with increasing the Mn means that the magnetic moment of Mn atoms at the 4b site couples ferromagnetically with that of the Mn atoms at the ordinary site (4a site).A solid straight line is drawn, assuming that the magnitude of the magnetic moment of Mn at the 4b site is the same as that of Mn at the 4a site, and the experimental values are in good agreement with the expected line[24].Here, the values of the magnetic moments (m) are used as m Mn = 3.719, m Ni = 0.277 and m In = −0.066µ B , which are obtained the first principle calculation[23].The T C values for all the specimens with x ≥ 16.2 are similar (the variation is <15 K) and they are independent to the composition.This behavior suggests that the T C is governed by the exchange interaction between Mn atoms at the 4a site, and the interaction by the Mn atoms at the 4b site does not affect the total exchange interaction in the system.This behavior of T C was studied earlier over a wide concentration region by Miyamoto et al.[25], who reported that T C decreases drastically with increases In concentration in Ni 50 Mn 50−y In y alloys with y > 25.Here, excess In substituted the Mn atoms at the 4a site, therefore, the decrease in T C is probably caused by the lack of Mn-Mn exchange interactions at the 4a site, if the magnetic moment of Mn atoms are assumed not to change.

Figure 3
Figure 3 indicates concentration dependences of saturation magnetization (Is) and TC for Ni50Mn50−xInx alloys with x ≥ 16.2, together with reported experimental values[22] and the theoretically calculated one for the stoichiometric composition[23].Here, Is is determined by linear extrapolation of the M 2 versus H/M curve to H/M = 0 (Arrott plot), from the data in Figure2a.Is increases almost linearly with decreasing In content, or in other words, with increasing Mn content.For the stoichiometric composition of Ni50Mn25In25 (= Ni2MnIn), the Ni atoms locate at the 8c site, and the Mn and In atoms at the 4a and 4b sites in the Wyckoff position, respectively.In the present series of the specimens, excess Mn substituted for In at the 4b site.Therefore, the increasing of Is with increasing the Mn means that the magnetic moment of Mn atoms at the 4b site couples ferromagnetically with that of the Mn atoms at the ordinary site (4a site).A solid straight line is drawn, assuming that the magnitude of the magnetic moment of Mn at the 4b site is the same as that of Mn at the 4a site, and the experimental values are in good agreement with the expected line[24].Here, the values of the magnetic moments (m) are used as mMn = 3.719, mNi = 0.277 and mIn = -0.066μB, which are obtained from the first principle calculation[23].The TC values for all the specimens with x ≥ 16.2 are similar (the variation is <15 K) and they are independent to the composition.This behavior suggests that the TC is governed by the exchange interaction between Mn atoms at the 4a site, and the interaction by the Mn atoms at the 4b site does not affect the total exchange interaction in the system.This behavior of TC was studied earlier over a wide concentration region by Miyamoto et al.[25], who reported that TC decreases drastically with increases In concentration in Ni50Mn50−yIny alloys with y > 25.Here, excess In substituted the Mn atoms at the 4a site, therefore, the decrease in TC is probably caused by the lack of Mn-Mn exchange interactions at the 4a site, if the magnetic moment of Mn atoms are assumed not to change.

Figure 3 .
Figure 3. Concentration dependences of the spontaneous magnetization (Is) evaluated from the magnetization curves in Figure2a, along with reported experimental and theoretically calculated values[22,23], and of the Curie temperature (TC) for Ni50Mn50−xInx alloys with x ≥ 16.2.The solid straight line for Is is simulated assuming that the excess Mn atoms have same magnetic moment as that of Mn at the ordinary sites and couples ferromagnetically[24].The solid line for TC is guide to the eye.

Figure 3 .
Figure 3. Concentration dependences of the spontaneous magnetization (I s ) evaluated from the magnetization curves in Figure2a, along with reported experimental and theoretically calculated values[22,23], and of the Curie temperature (T C ) for Ni 50 Mn 50−x In x alloys with x ≥ 16.2.The solid straight line for I s is simulated assuming that the excess Mn atoms have same magnetic moment as that of Mn at the ordinary sites and couples ferromagnetically[24].The solid line for T C is guide to the eye.

Figure 4 .
Figure 4. (a) C/T-T 2 plot for the specific heat (C) as a function of temperature (T) for (a) x ≤ 15 and (b) x ≥ 16.2 in Ni50Mn50−xInx alloys.Insets are C-T plots for each specimen.

Figure 4 .
Figure 4. (a) C/T-T 2 plot for the specific heat (C) as a function of temperature (T) for (a) x ≤ 15 and (b) x ≥ 16.2 in Ni 50 Mn 50−x In x alloys.Insets are C-T plots for each specimen.

Figure 5 .
Figure 5. Concentration dependences of the electronic specific heat coefficient (γ) and the Debye temperature (θD) for Ni50Mn50−xInx alloys, along with the reported theoretically calculated values[10] and reported ones for x = 0[11].The blue and light blue circles are θD in M phase and P phase, respectively, and the red and pink circles are γ in M phase and P phase, respectively.The four lines are guide to the eye.

Figure 5 .
Figure 5. Concentration dependences of the electronic specific heat coefficient (γ) and the Debye temperature (θ D ) for Ni 50 Mn 50−x In x alloys, along with the reported theoretically calculated values[10] and reported ones for x = 0[11].The blue and light blue circles are θ D in M phase and P phase, respectively, and the red and pink circles are γ in M phase and P phase, respectively.The four lines are guide to the eye.